Radio station market analysis

ABSTRACT

A radio station market analysis program extends Cume values for individual stations to multiple stations (for a particular geographic market, a particular demographic, and a particular daypart) according to the formula C=[1−Π i=1,n (1−C i /P)]*P, where n is the number of media stations, P is the population, and C i  is each Cume value. Cume values may be provided for a limited set of input dayparts from Arbitron and Nielson, and are translated to an arbitrary daypart. The arbitrary daypart can represent a sum of component dayparts in a proposed advertising schedule. The reach of the proposed advertising schedule can be further computed based on a hyperbolic function of spot count.

CROSS REFERENCE TO RELATED PATENTS

The present U.S. Utility Patent Application claims priority pursuant to35 U.S.C. §120, as a continuation, to the following U.S. Utility PatentApplication which is hereby incorporated herein by reference in itsentirety and made part of the present U.S. Utility Patent Applicationfor all purposes:

U.S. Utility application Ser. No. 12/687,355, entitled, “Method forComputing Reach of an Arbitrary Radio Advertising Schedule”, filed Jan.14, 2010, pending.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

NOT APPLICABLE

INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC

NOT APPLICABLE

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

The present invention generally relates to audience statistics, and morespecifically to methods and systems for computing statistics relating tostation audiences, particularly terrestrial radio stations.

2. Description of Related Art

Radio ratings are very important to many different divisions of a radiostation company, including radio station executives, advertising andmarketing departments, and program directors. Radio station executivesuse ratings statistics to help them evaluate the health of the company'sradio stations, as well as monitoring competitors and industry-widetrends. Advertisers and marketers depend on ratings to measure theeffectiveness of their advertising/marketing strategies and adapt tochanging market environments and fads. It is a program director'sresponsibility to not only have an intimate understanding of how ratingsare compiled and calculated, but also how to utilize these ratings in aneffort to adapt and innovate software solutions for varying marketcircumstances and business needs.

There are several standard types of statistics (ratings data) forresearching radio stations, including AQH (or AQHP), Cume, and primarydemographic. AQH stands for Average Quarter Hour (AQHP is AverageQuarter Hour Persons), and refers to the average number of peoplelistening to a radio station for at least five minutes in any quarterhour of a radio station's schedule. The number of people listening to anentire hour is not necessarily the sum of four quarter hours because ofduplication. However, some people may listen for more than a singlequarter hour. Cume is the total number of different (unique) personsthat listen to a radio station within a given daypart. A daypart is aset of times throughout a given week. For example, a daypart could beevery weekday (Monday through Friday) from 6:00 am until 10:00 am. Ifthe daypart is 15 minutes there is no difference between AQH and Cume.Primary demographic refers to various categories of consumers (listenersof a given radio station) such as gender or age.

Arbitron, Inc., is an organization which collects raw radio listenerdata and generates statistical information similar to the standardstatistics mentioned above. It is a media and marketing research firmwhich primarily serves media companies and advertisers/advertisingagencies who carry out ratings analysis based on the statistics.Arbitron selects random samples of the population throughout variousmetro areas in the United States, and participants keep a diary of theiractual listening times. Respondent-level data (RLD) is the raw datacollected by Arbitron, while the summary data set (SDS) is the variousstatistics calculated by Arbitron, which is derived from therespondent-level data and has only specifically-selected dayparts (40dayparts total).

Tapscan is a local market radio ratings software suite developed byArbitron, which is used by media planners (e.g., ad agencies) to decidewhere to place their clients' radio commercials. Some of the specificfeatures of Tapscan include ranking radio stations based on theirbroadcast hours, day, audiences, etc., using audience composition data(consumer demographics) to determine which radio stations are listenedto by what people, presenting cost and radio station data in differentways, providing access to customized demographics, geographies, daypartsand multibook averages, and determining a radio station's reach andfrequency by specific demographic, daypart, and spot level. Tapscan usesRLD and SDS, and other data sets such as Arbitron's Black Radio Data,Hispanic Radio Data, and Eastlan Radio Data.

Although Tapscan and other radio station ratings programs can provide areach value for a radio station, the reach provided is calculated basedon interpretation of listener statistics. Those interested in radiostation research might find a different source of reach useful, as wellas other statistics which are related to reach. The values of suchstatistics as AQH and Cume provided by Arbitron are calculated using alimited set of dayparts, which means that these values would bedifferent if an alternative set of dayparts was defined.

It would, therefore, be desirable to devise an improved method ofcalculating ratings data for radio stations. It would be furtheradvantageous if the method could effectively approximate differentratings statistics from previously collected data for arbitraryuser-specified schedules.

SUMMARY OF THE INVENTION

The foregoing objects are achieved in a method of extending Cume valuesfor individual media stations to multiple media stations, by receiving apopulation value and Cume values for each of the individual mediastations based on given ratings parameters, identifying a set ofmultiple media stations including two or more of the individual mediastations, and computing a Cume value C for the set of multiple mediastations according to the formula

$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )}} \rbrack*P}$

where n is the number of media stations in the set, P is the populationvalue, and C_(i) is each Cume value for an individual media station i inthe set, by executing program instructions in a computer system. Theratings parameters may include a particular geographic market, aparticular demographic, and a particular daypart, and the populationvalue may be the population of the particular demographic over theparticular geographic market. The Cume values for each of the individualmedia stations may be provided for a limited set of input dayparts (forexample from Arbitron or Nielson), and the Cume values can be translatedto an arbitrary daypart different from the input dayparts by identifyinga smallest one of the input dayparts that encompasses the arbitrarydaypart (the minimal parent), creating a list of Cume values whichinclude first Cume values for maximal input dayparts encompassed by thearbitrary daypart and second Cume values for intersections of thearbitrary daypart and selected input dayparts, and computing a desiredCume value for the arbitrary daypart according to a similar formula butsubstituting the Cume value of the minimal parent for the population P.The method can operate on first Cume values from a first vendor for afirst set of dayparts to provide a first output, and operate on secondCume values from a second vendor for a second set of dayparts differentfrom the first set to provide a second output. The arbitrary daypart canrepresent a sum of component dayparts in a proposed advertisingschedule. The reach of the proposed advertising schedule can be furthercomputed based on an inverse exponential function of spot count.

The above as well as additional objectives, features, and advantages ofthe present invention will become apparent in the following detailedwritten description.

The present invention may be better understood, and its numerousobjects, features, and advantages made apparent to those skilled in theart by referencing the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

FIG. 1 is a block diagram of a computer system programmed to carry outradio station ratings analysis in accordance with one implementation ofthe present invention;

FIG. 2 is a pictorial representation of a system used in accordance withone embodiment of the present invention for computing radio stationmarketing statistics;

FIG. 3 is a chart illustrating the logical flow for a process oftranslating and rolling up average quarter hour (AQH) and Cume values tocalculate various outputs for radio station ratings analysis inaccordance with one implementation of the present invention;

FIG. 4 is a chart illustrating the logical flow for a process ofcomputing Cume values for arbitrary dayparts in accordance with oneimplementation of the present invention;

FIG. 5 is a chart illustrating the logical flow for a process of rollingup Cume values over multiple radio stations in accordance with oneimplementation of the present invention; and

FIG. 6 is a graph illustrating an inverse exponential model forcomputing reach of an arbitrary radio advertising schedule in accordancewith one implementation of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The use of the same reference symbols in different drawings indicatessimilar or identical items.

With reference now to the figures, and in particular with reference toFIG. 1, there is depicted one embodiment 10 of a computer system inwhich the present invention may be implemented to carry out radiostation ratings analysis. Computer system 10 is a symmetricmultiprocessor (SMP) system having a plurality of processors 12 a, 12 bconnected to a system bus 14. System bus 14 is further connected to acombined memory controller/host bridge (MC/HB) 16 which provides aninterface to system memory 18. System memory 18 may be a local memorydevice or alternatively may include a plurality of distributed memorydevices, preferably dynamic random-access memory (DRAM). There may beadditional structures in the memory hierarchy which are not depicted,such as on-board (L1) and second-level (L2) or third-level (L3) caches.

MC/HB 16 also has an interface to peripheral component interconnect(PCI) Express links 20 a, 20 b, 20 c. Each PCI Express (PCIe) link 20 a,20 b is connected to a respective PCIe adaptor 22 a, 22 b, and each PCIeadaptor 22 a, 22 b is connected to a respective input/output (I/O)device 24 a, 24 b. MC/HB 16 may additionally have an interface to an I/Obus 26 which is connected to a switch (I/O fabric) 28. Switch 28provides a fan-out for the I/O bus to a plurality of PCI links 20 d, 20e, 20 f. These PCI links are connected to more PCIe adaptors 22 c, 22 d,22 e which in turn support more I/O devices 24 c, 24 d, 24 e. The I/Odevices may include, without limitation, a keyboard, a graphicalpointing device (mouse), a microphone, a display device, speakers, apermanent storage device (hard disk drive) or an array of such storagedevices, an optical disk drive, and a network card. Each PCIe adaptorprovides an interface between the PCI link and the respective I/Odevice. MC/HB 16 provides a low latency path through which processors 12a, 12 b may access PCI devices mapped anywhere within bus memory or I/Oaddress spaces. MC/HB 16 further provides a high bandwidth path to allowthe PCI devices to access memory 18. Switch 28 may provide peer-to-peercommunications between different endpoints and this data traffic doesnot need to be forwarded to MC/HB 16 if it does not involvecache-coherent memory transfers. Switch 28 is shown as a separatelogical component but it could be integrated into MC/HB 16.

In this embodiment, PCI link 20 c connects MC/HB 16 to a serviceprocessor interface 30 to allow communications between I/O device 24 aand a service processor 32. Service processor 32 is connected toprocessors 12 a, 12 b via a JTAG interface 34, and uses an attentionline 36 which interrupts the operation of processors 12 a, 12 b. Serviceprocessor 32 may have its own local memory 38, and is connected toread-only memory (ROM) 40 which stores various program instructions forsystem startup. Service processor 32 may also have access to a hardwareoperator panel 42 to provide system status and diagnostic information.

In alternative embodiments computer system 10 may include modificationsof these hardware components or their interconnections, or additionalcomponents, so the depicted example should not be construed as implyingany architectural limitations with respect to the present invention.

When computer system 10 is initially powered up, service processor 32uses JTAG interface 34 to interrogate the system (host) processors 12 a,12 b and MC/HB 16. After completing the interrogation, service processor32 acquires an inventory and topology for computer system 10. Serviceprocessor 32 then executes various tests such as built-in-self-tests(BISTs), basic assurance tests (BATs), and memory tests on thecomponents of computer system 10. Any error information for failuresdetected during the testing is reported by service processor 32 tooperator panel 42. If a valid configuration of system resources is stillpossible after taking out any components found to be faulty during thetesting then computer system 10 is allowed to proceed. Executable codeis loaded into memory 18 and service processor 32 releases hostprocessors 12 a, 12 b for execution of the program code, e.g., anoperating system (OS) which is used to launch applications and inparticular the radio station statistical application of the presentinvention, results of which may be stored in a hard disk drive of thesystem (an I/O device 24). While host processors 12 a, 12 b areexecuting program code, service processor 32 may enter a mode ofmonitoring and reporting any operating parameters or errors, such as thecooling fan speed and operation, thermal sensors, power supplyregulators, and recoverable and non-recoverable errors reported by anyof processors 12 a, 12 b, memory 18, and MC/HB 16. Service processor 32may take further action based on the type of errors or definedthresholds.

While the illustrative implementation provides program instructionsembodying the present invention on a disk drive of computer system 10,those skilled in the art will appreciate that the invention can beembodied in a program product utilizing other computer-readable storagemedia. The program instructions may be written in the C++ programminglanguage for a Windows 7 environment or in other programming languagessuitable for other operating system platforms. Computer system 10carries out program instructions for a radio station ratings analysisprocess that uses novel computational techniques to manage statisticaldata. Accordingly, a program embodying the invention may includeconventional aspects of various statistical tools, and these detailswill become apparent to those skilled in the art upon reference to thisdisclosure.

FIG. 2 is a pictorial representation of a station marketing analysissystem 44 used in accordance with one embodiment of the presentinvention for computing radio station marketing statistics. Stationmarketing analysis system 44 employs an engine 45 denoted “AudiencePro”which may be implemented through execution of program instructions oncomputer system 10. AudiencePro engine 45 can collect various types ofinformation, including (but not limited to) raw Arbitron data 46, rawNielson data 47, station list and schedules 48, and spot prices 49. RawArbitron data 46 includes data such as AQH, Cume, and marketpopulations, for a limited set of summary dayparts (input/Arbitrondayparts). For example, Arbitron provides AQH values for the daypartsMonday-Friday 5-6 a.m., Monday-Friday 6-7 a.m., . . . , Monday-Fridaymidnight-1 a.m., and larger granularities such as Monday-Friday 1-5 a.m.The same dayparts are provided for Saturday and Sunday, individually.One daypart is even Monday-Sunday 6 a.m.-6 a.m. (the entire week). RawNielson data 47 is similar to raw Arbitron data 46 but is provided for adifferent set of dayparts. Station list and schedules 48 providesAudiencePro engine 45 with a list of stations and various advertisingschedules including arbitrary (user-defined) sets of dayparts as desiredby the client for a particular marketing campaign. Radio stations selltheir airtime according to dayparts. A simple daypart lineup might be: 6am-10 am, 10 am-3 pm, 3 pm-7 pm, and 7 pm-midnight. AudiencePro engine45 can also receive information regarding spot prices 49 from the clientor other sources such as a yield management system which automatespricing. A spot price is the current price at which a particularcommodity (in this example, radio advertising time) can be bought orsold. These information sources can be in operative communication withAudiencePro engine 45 by a variety of means, such as public or privatewired or wireless (radio or cellular) networks including the Internet,satellite, public switched telephone network (PSTN), or any combinationof the foregoing, including some form of direct wiring. When AudienceProengine 45 is deployed in a client environment, it can download allArbitron or Nielson data needed for an extended period of time and cacheit on the client machine (computer system 10).

After processing inputs from the information sources, AudiencePro engine45 produces delivery information 50 which can include a wide variety ofratings-related statistics. Delivery information can be provided in avariety of forms to any output device (i.e., I/O device 24) of computersystem 10, such as a display device or printer. In a preferredembodiment delivery information 50 includes:

-   -   Gross Impressions (“GI,” the sum of individual AQH numbers,        rolled up across stations and dayparts);    -   CPM (Cost Per Thousand=price/GI*10001);    -   GRP (Gross Rating Points=GI/population*100);    -   CPP (Cost Per Point=price/GRP);    -   Reach (can be derived in conjunction with FIG. 6 below);    -   % Market Reach (Reach*100/population);    -   Frequency (GI/Reach); [0035] CPMNR (CPM Net        Reach=price/Reach*1000);    -   AQH (for the daypart in question, does not depend on spot        count);    -   AQH Rating (AQH/population*100);    -   Cume (for the daypart in question, does not depend on spot        count);    -   Cume Rating (Cume/population*100).

AudiencePro engine 45 can maintain this output data and more (includinginput data and intermediate data) in multi-dimensional arrays ormatrices with different variables indexed as appropriate, such as bybook, market, demographic, station, Arbitron daypart, or client daypart.

As explained further below, in order to produce these outputsAudiencePro engine 45 executes several calculations including computingthe Cume of an arbitrary daypart from the Cume of a limited set ofdayparts, and computing a Cume for multiple stations from Cume values ofindividual stations. The outputs of AudiencePro engine 45 areaccordingly dependent on various user inputs, such as the list ofstations, demographic, flight dates and schedule for each desiredstation (including specific dayparts, spot counts, and any weightingadjustments).

FIG. 3 is a flow chart for a process of translating and rolling up AQHand Cume values to calculate the various outputs of AudiencePro engine45 and particularly Reach, in accordance with one implementation of thepresent invention. In FIG. 3 and the figures that follow, AQH isrepresented by the letter “S”, and Cume is represented by the letter“C”. The radio station ratings analysis process begins when computersystem 10 receives information from the various sources, particularly Sand C of all available stations for limited (Arbitron or Nielson)dayparts, a station list, and a proposed schedule including client(AudiencePro) dayparts (51). The radio station ratings application ofthe present invention can consolidate the data streams from multiplevendors such as Arbitron and Nielson to present a single interface tothe user. In this manner the system can switch between sets of inputdata to provide output based on a selected vendor. The input S valuesfor each client station are then translated from the limited dayparts tothe client dayparts (52). If the client daypart is contained in an inputdaypart, then the S value from that input daypart will simply be usedfor the translation. If instead the client daypart is not contained inan input daypart, then the smallest set of input dayparts that containthe client daypart will be used for the translation. In this case, the Svalue for the client daypart is the weighted average of S values for theinput dayparts in this set. The average is weighted by the portion ofthe client daypart contained in each input daypart used. After S valuesare translated, they can be extended (rolled up) across multiple(client) dayparts and multiple stations (54). To roll up the S values,gross impressions (GI) are added up across order lines which can spanmultiple dayparts and multiple stations. Then, the rolled up S for theschedule (which can span multiple dayparts and stations) is the total GIdivided by the number of spots.

Once these intermediate AQH computations are complete, similarcomputations are performed for Cume. The input C values for each clientstation are translated from the limited dayparts to the client dayparts(56). A preferred computation for this C translation is discussedfurther below in conjunction with FIG. 4. After C values are translated,they can be rolled up across multiple (client) dayparts and multiplestations (58). Rolling up C values across dayparts is accomplished usedthe same algorithm for C value translation; the input daypart for thealgorithm is given as the sum of dayparts in the proposed schedule. Apreferred computation for rolling up C values across stations isdiscussed further below in conjunction with FIG. 5. Delivery information50 is then computed according the formulas given above (60), and theprocess is complete. The translation and rolling up of S and C valuescan introduce inaccuracies to varying degrees but the resulting outputsare still considered excellent approximations for marketing and researchpurposes.

In some embodiments the translation of C values from a limited set ofdayparts to an arbitrary daypart (56) is accomplished by the processillustrated in the flow chart of FIG. 4. This process begins whencomputer system 10 identifies the smallest input daypart which stillcovers an entire (user-specified) daypart, referred to herein as theminimal parent. A list of C values is created and opened at firstwithout any entries (64). The process loops through all of the inputdayparts, identifying in each iteration the maximal (longest) inputdaypart that is still within the arbitrary daypart. The C value of themaximal input daypart is added to the list, and the maximal inputdaypart for this iteration is subtracted from the arbitrary daypart(66). The process then loops through selected input dayparts to find anyintersections (overlaps) with the remaining arbitrary daypart. In theimplementation for Arbitron input data, the selected input dayparts areM-F AM, Sat AM, Sun AM, M-F MD, Sat MD, Sun MD, M-F PM, Sat PM, Sun PM,M-F EV, Sat EV, Sun EV, and M-Su ON. If an intersection is found a Cvalue is computed for it and added to the list. The intersection isremoved from the arbitrary daypart, so any intersections are mutuallyexclusive (68). The C values for the intersections may be computed invarious manners, preferably using a hyperbolic fit. The fit uses ahyperbola of the form y=Ax/(Bx+C) that passes through the points (x₁,y₁)and (x₂,y₂), where x₁ is 1, y₁ is the AQH of the input daypart which isbeing subtracted from the arbitrary daypart, x₂ is the number of hoursin the input daypart which is being subtracted from the arbitrarydaypart, y.sub.2 is the Cume of the input daypart which is beingsubtracted from the arbitrary daypart, A is y₁*y₂, B is(x₂*y₁−x₁*y₂)/(x₂−x₁), and C is x₂*y₂−Bx₁.

A binomial method can be used to calculate C for the arbitrary daypartbased on the compiled C values in the list (70). This binomial method isthe same as that described below in conjunction with FIG. 5, but the Cvalue of the minimal parent is substituted for the population, i.e., theCume value C _(arbitrary) for the arbitrary daypart is

$ {C_{arbitrary} = {1 - {\prod\limits_{{j - 1},m}^{\;}\; ( {1 - \frac{C_{j}}{C_{small}}} )}}} \rbrack*C_{small}$

where m is the number of Cume values in the list, C_(small) is the Cumevalue of the smallest input daypart, and C_(j) is each Cume value j inthe list. The arbitrary daypart can represent a sum of componentdayparts in a proposed advertising schedule.

In a simplified example, consider input dayparts which include afour-hour daypart of Monday-Sunday 6-10 a.m., and 1-hour dayparts ofMonday-Sunday 6-7 a.m., Monday-Sunday 7-8 a.m., Monday-Sunday 8-9 a.m.,and Monday-Sunday 9-10 a.m. The client is considering a schedule whichincludes the 3-hour daypart of Monday-Sunday 6-9 a.m. In this case, theminimal parent would be the four-hour daypart, and the accumulated inputdayparts would be Monday-Sunday 6-7 a.m., Monday-Sunday 7-8 a.m., andMonday-Sunday 8-9 a.m. The binomial calculation would then operate onthe three C values for these three input dayparts, using the C value ofthe four-hour daypart as the population.

This binomial calculation is shown in further detail in the flow chartof FIG. 5, but for rolling up C values across multiple stations ratherthan multiple dayparts. The C values for individual stations are basedon given ratings parameters, e.g., a particular geographic market, aparticular demographic, and a particular daypart. The process beginswhen computer system 10 receives those C values and associatedpopulations (P) for a given market over a specific demographic (72). Theprocess then identifies a set of the multiple media stations based onuser input (74). These stations have C values denoted C_(i). Theprobability that a given person in the demographic is listening to thegiven station at a given time can be expressed as C_(i)/P. Accordingly,the probability that the person is not listening to the station at thegiven time is 1−(C_(i)/P). It also follows that the probability that theperson is not listening to any of the stations in the market at thegiven time is

$\prod\limits_{{i - 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )$

where n is the number of stations in the set, and that the probabilitythat the person is listening to at least one of the identified stationsin the market is

$1 - {\prod\limits_{{i - 1},n}^{\;}\; {( {1 - \frac{C_{i}}{P}} ).}}$

The final Cume for the multiple media stations as a group can thus becomputed as

$\begin{matrix}{\lbrack {1 - {\prod\limits_{{i - 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )}} \rbrack*{P.}} & (76)\end{matrix}$

As noted above, the various translated and rolled up S and C values canbe used to generate a variety of outputs. One audience statistic that isvery important to marketers/advertisers is reach. In some embodimentsthe present invention uses an inverse exponential model to compute thereach of an arbitrary radio advertising schedule, i.e., the estimatednumber of different people actually hearing an ad. FIG. 6 illustratesthis model which can be constructed according to the formula

Reach=n*S*C/[(n*S)+C−S],

where n is the number of spots in a given schedule, and S and C are theaggregate (translated and rolled up) values for the schedule. When usingthis formula, for just one radio advertising spot the reach is S, whilefor a very large number of spots the reach is C.

Although the invention has been described with reference to specificembodiments, this description is not meant to be construed in a limitingsense. Various modifications of the disclosed embodiments, as well asalternative embodiments of the invention, will become apparent topersons skilled in the art upon reference to the description of theinvention. For example, the invention is applicable to other mediastations besides terrestrial radio, such as internet radio, cable orbroadcast television, or satellite. It is therefore contemplated thatsuch modifications can be made without departing from the spirit orscope of the present invention as defined in the appended claims.

What is claimed is:
 1. A computer implemented method comprising:obtaining input CUME values for each of a plurality of individual radiostations, wherein the input CUME values represent CUME values associatedwith a limited set of input dayparts, by executing program instructionsin a computer system; and translating the input CUME values associatedwith a plurality of the input dayparts to determine an output CUME valueassociated with an arbitrary daypart, different from the input dayparts,by executing program instructions in a computer system.
 2. The method ofclaim 1, wherein the translating comprises: identifying a minimal parentdaypart, wherein the minimal parent daypart corresponds to the smallestone of the input dayparts that encompasses the arbitrary daypart, byexecuting program instructions in a computer system; determining atleast a first Cume value associated with a maximal input daypartencompassed by the arbitrary daypart, by executing program instructionsin a computer system; and determining at least a second Cume valueassociated with an intersection of the arbitrary daypart and selectedinput dayparts, by executing program instructions in a computer system.3. The method of claim 2, further comprising: computing, by executingprogram instructions in a computer system, an output Cume value for thearbitrary daypart according to the following formula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P_{cumesubstitute}}} )}} \rbrack*P_{cumesubstitute}}$where n is the number of media stations included in a set of mediastations comprising the plurality of individual radio stations,P_(cumesubstitue) is the CUME value of the minimal parent daypart, andC_(i) is each CUME value for an individual media station i.
 4. Themethod of claim 3, further comprising: calculating, by executing programinstructions in a computer system, a CUME value for the set of mediastations based on the following formula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )}} \rbrack*P}$where n is the number of media stations included in the set of mediastations, P is the population value, and C_(i) is each CUME value for anindividual media station i.
 5. The method of claim 2, furthercomprising: adding the CUME value of the arbitrary daypart to a list, byexecuting program instructions in a computer system; removing themaximal input daypart from the arbitrary daypart, by executing programinstructions in a computer system; adding the Cume value of theintersection to the list, by executing program instructions in acomputer system; and removing the intersection from the arbitrarydaypart, by executing program instructions in a computer system.
 6. Themethod of claim 1, wherein the arbitrary daypart represents a sum ofcomponent dayparts in a proposed advertising schedule.
 7. The method ofclaim 6, further comprising; computing, by executing programinstructions in a computer system, a reach of the proposed advertisingschedule based on an inverse exponential function of spot count.
 8. Acomputer system comprising: one or more processors to process programinstructions; a memory device coupled to said one or more processors;and program instructions residing in said memory device, said program ofinstructions configured to implement a method including: obtaining inputCUME values for each of a plurality of individual radio stations,wherein the input CUME values represent CUME values associated with alimited set of input dayparts; and translating the input CUME valuesassociated with a plurality of the input dayparts to determine an outputCUME value associated with an arbitrary daypart, different from theinput dayparts.
 9. The computer system of claim 8, wherein thetranslating comprises: identifying a minimal parent daypart, wherein theminimal parent daypart corresponds to the smallest one of the inputdayparts that encompasses the arbitrary daypart; determining at least afirst Cume value associated with a maximal input daypart encompassed bythe arbitrary daypart; and determining at least a second Cume valueassociated with an intersection of the arbitrary daypart and selectedinput dayparts.
 10. The computer system of claim 9, wherein the methodincludes: computing an output Cume value for the arbitrary daypartaccording to the following formula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P_{cumesubstitute}}} )}} \rbrack*P_{cumesubstitute}}$where n is the number of media stations included in a set of mediastations comprising the plurality of individual radio stations,P_(cumesubstitute) is the CUME value of the minimal parent daypart, andC_(i) is each CUME value for an individual media station i.
 11. Thecomputer system of claim 10, wherein the method includes: computing aCUME value for the set of media stations based on the following formula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )}} \rbrack*P}$where n is the number of media stations included in the set of mediastations, P is the population value, and C_(i) is each CUME value for anindividual media station i.
 12. The computer system of claim 9, whereinthe method includes: adding the CUME value of the arbitrary daypart to alist; removing the maximal input daypart from the arbitrary daypart;adding the Cume value of the intersection to the list; and removing theintersection from the arbitrary daypart.
 13. The computer system ofclaim 8, wherein the arbitrary daypart represents a sum of componentdayparts in a proposed advertising schedule.
 14. The computer system ofclaim 13, further comprising; computing a reach of the proposedadvertising schedule based on an inverse exponential function of spotcount.
 15. A computer program product comprising: a non-transitorycomputer-readable storage medium; and program instructions residing insaid medium, said program instructions including: at least oneinstruction to obtain input CUME values for each of a plurality ofindividual radio stations, wherein the input CUME values represent CUMEvalues associated with a limited set of input dayparts; and at least oneinstruction to translate the input CUME values associated with aplurality of the input dayparts to determine an output CUME valueassociated with an arbitrary daypart, different from the input dayparts.16. The computer program product of claim 15, wherein the translatingcomprises: at least one instruction to identify a minimal parentdaypart, wherein the minimal parent daypart corresponds to the smallestone of the input dayparts that encompasses the arbitrary daypart; atleast one instruction to determine at least a first Cume valueassociated with a maximal input daypart encompassed by the arbitrarydaypart; and at least one instruction to determine at least a secondCume value associated with an intersection of the arbitrary daypart andselected input dayparts.
 17. The computer program product of claim 16,wherein the method includes: at least one instruction to compute anoutput Cume value for the arbitrary daypart according to the followingformula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P_{cumesubstitute}}} )}} \rbrack*P_{cumesubstitute}}$where n is the number of media stations included in a set of mediastations comprising the plurality of individual radio stations,P_(cumesubstitue) is the CUME value of the minimal parent daypart, andC_(i) is each CUME value for an individual media station i.
 18. Thecomputer program product of claim 17, wherein the method includes: atleast one instruction to compute a CUME value for the set of mediastations based on the following formula:$C = {\lbrack {1 - {\prod\limits_{{i = 1},n}^{\;}\; ( {1 - \frac{C_{i}}{P}} )}} \rbrack*P}$where n is the number of media stations included in the set of mediastations, P is the population value, and C_(i) is each CUME value for anindividual media station i.
 19. The computer program product of claim16, wherein the method includes: at least one instruction to add theCUME value of the arbitrary daypart to a list; at least one instructionto remove the maximal input daypart from the arbitrary daypart; at leastone instruction to add the Cume value of the intersection to the list;and at least one instruction to remove the intersection from thearbitrary daypart.
 20. The computer program product of claim 15, whereinthe arbitrary daypart represents a sum of component dayparts in aproposed advertising schedule.